eprintid: 10193041
rev_number: 12
eprint_status: archive
userid: 699
dir: disk0/10/19/30/41
datestamp: 2024-06-04 13:31:12
lastmod: 2024-11-19 14:47:31
status_changed: 2024-06-04 13:31:12
type: article
metadata_visibility: show
sword_depositor: 699
creators_name: Kosloff, Zemer
creators_name: Soo, Terry
title: Sinai factors of nonsingular systems: Bernoulli shifts and Anosov flows
ispublished: inpress
divisions: UCL
divisions: B04
divisions: C06
divisions: F61
note: This version is the author-accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
abstract: We show that a totally dissipative system has all nonsingular systems as
factors, but that this is no longer true when the factor maps are required to
be finitary. In particular, if a nonsingular Bernoulli shift satisfies the
Doeblin condition, and has a limiting marginal distribution p, then it cannot
have, as a finitary factor, an independent and identically distributed (iid)
system of entropy larger than H(p); on the other hand, we show that iid systems
with entropy strictly lower than H(p) can be obtained as finitary factors of
these Bernoulli shifts, extending Keane and Smorodinsky's finitary version of
Sinai's factor theorem to the nonsingular setting. As a consequence of our
results we also obtain that every transitive twice continuously differentiable
Anosov diffeomorphism on a compact manifold, endowed with volume measure, has
iid factors, and if the factor is required to be finitary, then the iid factor
cannot have Kolmogorov-Sinai entropy greater than the measure-theoretic entropy
of a Sinai-Ruelle-Bowen measure associated with the Anosov diffeomorphism.
date: 2024-12
date_type: published
official_url: https://doi.org/10.3934/jmd.2024016
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 1906982
doi: 10.3934/jmd.2024016
lyricists_name: Soo, Terry
lyricists_id: TSOOX84
actors_name: Soo, Terry
actors_id: TSOOX84
actors_role: owner
full_text_status: public
publication: Journal of Modern Dynamics
volume: 20
pagerange: 597-634
issn: 1930-5311
citation:        Kosloff, Zemer;    Soo, Terry;      (2024)    Sinai factors of nonsingular systems: Bernoulli shifts and Anosov flows.                   Journal of Modern Dynamics , 20    pp. 597-634.    10.3934/jmd.2024016 <https://doi.org/10.3934/jmd.2024016>.    (In press).    Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10193041/1/kosloff-soo-jmd-rev-final.pdf